Problem 118 - Chemistry Central Science

Question

A gas forms when elemental sulfur is heated carefully with AgF. The initial product boils at \(15^{\circ} \mathrm{C}\). Experiments on several samples yielded a gas density of \(0.803 \pm 0.010 \mathrm{~g} / \mathrm{L}\) for the gas at \(150 \mathrm{~mm}\) pressure and \(32{ }^{\circ} \mathrm{C}\). When the gas reacts with water, all the fluorine is converted to aqueous HF. Other products are elemental sulfur, \(S_{8}\), and other sulfur-containing compounds. A 480 -mL sample of the dry gas at \(126 \mathrm{~mm}\) pressure and \(28^{\circ} \mathrm{C}\), when reacted with \(80 \mathrm{~mL}\) of water, yielded a \(0.081 \mathrm{M}\) solution of HF. The initial gaseous product undergoes a transformation over a period of time to a second compound with the same empirical and molecular formula, which boils at \(-10^{\circ} \mathrm{C}\). (a) Determine the empirical and molecular formulas of the first compound formed. (b) Draw at least two reasonable Lewis structures that represent the initial compound and the one into which it is transformed over time. (c) Describe the likely geometries of these compounds, and estimate the single bond distances, given that the \(\mathrm{S}-\mathrm{S}\) bond distance in \(\mathrm{S}_{8}\) is \(2.04 \mathrm{~A}\) and the \(\mathrm{F}-\mathrm{F}\) distance in \(\mathrm{F}_{2}\) is \(1.43 \mathrm{~A}\).

Step-by-Step Solution

Answer

The empirical and molecular formulas of the first compound formed are both SF₂. Both the initial compound and the one into which it is transformed over time have the same Lewis structure, with Sulfur (S) at the center and two Fluorine (F) atoms bonded to it. The geometry of these compounds is bent, with an approximate bond angle of 105°. The S-F bond distance can be roughly estimated as 1.74 A, but accurate data should be used to get a precise value.

Step 1: a.1 Calculate moles of HF produced

We are given that a 480 mL sample of the gas reacted with 80mL of water, yielded a 0.081M solution of HF. To calculate the moles of HF produced in the reaction, we use the formula: Moles of HF = Molarity × Volume = \(0.081M * 0.080L = 0.00648 mol\)

Step 2: a.2 Calculate moles of F₂ in the initial gas sample

Since one mole of HF will be formed from one mole of F₂ in the initial gas sample, the moles of F₂ in the initial sample must be equal to moles of HF produced: Moles of F₂ = 0.00648 mol

Step 3: a.3 Calculate moles of the initial gas sample

We are given the gas density in \(g/L\), the pressure, and the temperature of the initial gas sample (pressure: \(150 \mathrm{~mm}\), temperature: \(32 ^{\circ}\mathrm{C}\)). First, let's convert the pressure to atm: atm = \(\frac{150mm}{760 mm/atm} = 0.1974 atm\) Then, we can use the Ideal Gas Law to find the moles of the initial gas sample: n = \(\frac{PV}{RT}\) where P is the pressure, V is the volume, R is the gas constant (0.08206 L·atm/mol·K), and T is the temperature (in Kelvin). T(K) = T(°C) + 273.15 = 32 + 273.15 = 305.15 K Substituting values, we get: n = \(\frac{(0.1974 atm)(0.480 L)}{(0.08206 L·atm/mol·K)(305.15 K)}\) = 0.00324 mol

Step 4: a.4 Calculate the empirical formula

We know there are 0.00648 moles of F₂ in the initial gas sample and 0.00324 moles of the gas. Therefore, the mole ratio of F₂ to gas sample is: 2:1 So we can infer that the empirical formula is SF₂.

Step 5: a.5 Calculate mass and molecular formula

Now let's calculate the molar mass of the initial gas sample using the given density of 0.803 g/L at 150 mm pressure and 32°C. Molar mass = Density × Molar volume Molar volume = PV/RT = 1 mol × 22.414 L/mol = 22.414 L Now, we can find the molar mass: Molar mass = \(0.803g/L * 22.414L = 18.0g/mol\) Since the molar mass calculated is the nearly equal to the molar mass of the empirical formula, SF₂ (32.1 g/mol for S and 38.0 g/mol for two F atoms), the molecular formula for the initial compound is also SF₂. ##Step 2: Draw Lewis structures and describe geometries##

Step 6: b. Draw Lewis structures

The initial compound is SF₂. In order to draw the Lewis structures, let's count the valence electrons. Sulfur has 6 valence electrons, while fluorine has 7 valence electrons. So, for the initial compound, we have 6x1 + 7x2 = 20 valence electrons. Sulfur will be central as it has a lower electronegativity than fluorine. Sulfur will have two single bonds, one to each fluorine atom, and two lone pairs of electrons. Both the initial gaseous product and the second compound have the same Lewis structure: F ' S ' ' F

Step 7: c. Describe geometries and estimate bond distances

The VSEPR (Valence Shell Electron Pair Repulsion) model predicts that the geometry of SF₂ will be bent because of the presence of two lone pairs around the central S atom. The bond angle between F-S-F would be approximately 105°. To estimate the bond distances, we can use the given bond distances of S-S and F-F, which are 2.04 A and 1.43 A, respectively. We can assume the S-F bond distance would be somewhere between these two values, due to varying electronegativity in the S and F atoms. Thus a rough estimate of the S-F bond distance might be the average of the two values, (2.04 A + 1.43 A)/2 = 1.74 A. However, experimental data should be used to get a more accurate value. To summarize the answer: (a) The empirical and molecular formulas of the first compound formed are both SF₂. (b) Both the initial compound and the one into which it is transformed over time have the same Lewis structure, with Sulfur (S) at the center and two Fluorine (F) atoms bonded to it. (c) The geometry of these compounds is bent, with an approximate bond angle of 105°. The S-F bond distance can be roughly estimated as 1.74 A, but accurate data should be used to get a precise value.

Key Concepts

Empirical and Molecular Formulas

Understanding the empirical and molecular formulas is crucial in identifying substances and their compositions. The empirical formula provides the simplest whole-number ratio of elements in a compound. For SF₂, it shows that for every sulfur atom, there are two fluorine atoms.

The molecular formula tells us the exact number of each type of atom in a molecule. In some cases, the empirical and molecular formulas are the same, as seen in SF₂. This means the simplest ratio exactly represents one molecule's composition.

To determine these formulas, we often start by finding the molar mass using data like gas density and the ideal gas law as tools to measure sample components. Calculating the moles from measurements, like volume or concentration, helps us decipher the compound's precise structure.

Ideal Gas Law

The Ideal Gas Law is a fundamental equation that connects the physical properties of gases. Its formula is given by \(PV = nRT\), where:

• \(P\) is the pressure
• \(V\) is the volume
• \(n\) is the number of moles
• \(R\) is the gas constant
• \(T\) is the temperature in Kelvin

This equation is powerful because it helps estimate the moles of gas involved in a reaction when pressure, volume, and temperature are known. It stands as a vital tool for chemists to infer how gases behave under different conditions.

In practical applications, like the exercise provided, it was used to deduce the moles of the gas using pressure (converted from mmHg to atm) and temperature (converted to Kelvin). This step is crucial for understanding reactions involving gases.

Lewis Structures

Lewis Structures are visual representations that show the arrangement of valence electrons around atoms in a molecule. They are key to understanding molecular composition and bonds.

In SF₂'s case, sulfur is the central atom, flanked by two fluorine atoms. Sulfur donates two electrons to form bonds with fluorine, each contributing one electron for a complete pair. Around sulfur, there are two lone pairs, reinforcing the molecule's geometry by exerting repulsive forces that influence its shape.

The value of Lewis structures lies in their ability to display electron distributions and aid in the prediction of molecular properties like polarity and reactivity.

Molecular Geometry

Molecular Geometry focuses on the 3D arrangement of atoms in a molecule. This geometry influences the molecule's physical properties and reactions.

For SF₂, the molecular geometry is bent due to two lone pairs on the sulfur atom that push the fluorine atoms downwards. This arrangement results in a bond angle slightly less than the typical tetrahedral angle, at around 105°. Understanding these angles helps predict molecular behavior, such as dipole moments and interactions with other molecules.

Additionally, bond distances provide insights into molecular dimensions. The estimated bond distances, like 1.74 Å for the S-F bond, highlight variations in atomic size and influence molecular structure characteristics.